What would be worse for American Apparel: filing for Chapter 11 or leaving it under the control of Dov Charney?

That’s the question confronting the cash-strapped retailer’s board of directors as it considers accepting a $10 million equity infusion that could give embattled CEO Charney breathing room and stave off bankruptcy, sources told The Post.

Charney — who lately has been fending off a series of sex-harassment suits, one of which accused him of keeping a former employee as a sex slave — has become exasperated as the company’s board has waffled over a rescue financing package that was offered last week, sources said.

“You have to question whether the board is thinking clearly here, given their fiduciary duty to shareholders,” said one source close to the situation. “The alternative could be much worse.”

Sources said proposed terms of the financing are expected to dilute the company’s current shareholders — with the possible exception of Charney. That’s because a proposed “earn-out” provision would give Charney, who is the company’s majority shareholder, options to acquire additional shares if the stock appreciates in the future, according to one source.

The bigger concern among some directors, however, is that the deal could bolster Charney’s position as he tries to reassert control over American Apparel’s struggling stores.

“There are some who believe that [Charney] needs to give up financial control of the company,” according to one source briefed on the board’s recent deliberations. “You could say that Dov has a history of spending money like a drunken sailor.”

Board members contacted by The Post declined to comment or didn’t respond to requests for comment.

The $10 million cash infusion, which is being offered by a deep-pocketed private investor based in Canada, could be followed by an additional injection of $15 million in the coming weeks, according to people briefed on the situation.

At least two outside investors, including the Canadian investor, are in negotiations to lend cash to American Apparel in deals brokered by the investment bank Rothschilds, sources said.

In addition, one source indicated that Charney, who last month pumped $1.8 million into the retailer, may pony up additional equity himself.

While the financing could be approved as soon as today, some fear it could evaporate nearly as quickly. Bank of America, which supplies the company’s revolving credit line, has been asking for additional “excess availability” of cash on American Apparel’s balance sheet, according to one source.

“You could see half of the $10 million disappear instantly for that reason alone,” according to the source. james.covert@nypost.com